Apparatus for measuring liquids.



H. H. sumo', DEC'D.. vjsumo. AnMxmsTRAToR. APPARATUS FOR I VH;`AS URING LIQUIDS.

APPLICATION F|LED.OCT.3| |913. v

A 'Patented May11,1915.

X A i.

/ ffy .Herbe/7507i@ UNITED STATES PATENT oEEioE.l

HARRY HERBERT SUTRO, DECEASED, BY VICTOR SUTRO, ADMINISTRATOR, OF NEW YORK, N. Y., ASSIGNOR TO L.` M. BOOTH COMPANY, A CORPORATION 0F NEW YORK.

APPARATUS FOR MEASIURING- LIQUIDS.

Original application led .Tune 1, 190.9, Serial No. 499,559. Divided and 1913. Serial No. 793,209.

This application is filed as a division of I application of Harry. Herbert Sutro for patent for improvements in water softening devices, filed J une 1, 1909, Serial No. 499,559 (patented Nov. 4l, 1913, No. 1,077,316).

Thisinvention relates to improvements in apparatus for measuring'liquids, and the.

object of myinvention is t o provide an apparatus for measuring liquids havlng a discharge outlet so formed that the flow of liquid therethrough will bein direct proportion to the height of liquidabove apredetei-mined point.

The other objects and features ofmy in-- vention are particularly described in the specification and appended claims.

Inv the accompanying drawings,'Figure l is a diagrammatic view illustrating mathematical demonstration of the theory of the improved weir. Fig. 2 is a general view showing the application of the invention to a liquid container.

Similar reference characters designate corresponding parts throughout the several figures of the drawings.

It will be understood that many changes may be made in the apparatus without departing from the spirit or scope'of my invention.

apparatus consists of a liquid container 1, into whichthe liquid to be measured is discharged, providedi with a dischargeorifice 2 in one of the walls thereof, such discharge orifice being of such shape that the ,flow of liquid therethrough will be in direct proportion to the height of the liquid above a fixed point. y v. 'f v In the preferable form of the invention, a distinct feature thereof resi'desfinhaving a `minimum operativeflevel ,above-thegdatum' level and a .bottom level below the datum Specification of Letters'Patent.

'tangle AOLK.

Patented May 11, 19115.

this application ined oetoblers;

level, in combination with a continuous curve'extending from the minimum operative .level to the maximum operative level, the width of the notch above the minimum operative level being'such that the flow of liquid therethrough will at all levels above the minimum level be in direct proportion to the height of liquid above the datum level. In the illustration shown in the drawings, the bottom level of the notch is designated by the letters AfK, the minimum operative level by the letters X-X, and the datum llevel by the letters M-N, with the distance between the bottom of the notch and the minimum operativelevel designated by the reference letter a To fully illustrate the mathematical principles underlying a weir notch having these characteristics, the following mathematical demonstration is given in explanation thereof:

Given: A weir opening composedV of the rectangle AOLK, and the upper curved portion bounded by the straight line AU and the curve LU lying above the Vrectangle vAOLK.

through the rectangle AOLK under a head la above` the top of the rectangle, plus the discharge (Q2) through the portion of the weir above the line XX. A

For convenience of calculation and prac- .tical operation the datum line MN is taken a distance ?a above the base AK ofthe rec- From the fundamental laws'of hydraulics the discharge fof the rectangle AOLK is found to be,

where cis the vcoeflicient lof discharge of the orifice, usually taken as .62, and theother letters have the signicance indicated on the accompanying' drawing, 'g?? being thel measze cjz/ ybeing the area of the strip and c bein the coelioient of discharge above mentione Applying the methods and. notation of the integral calculus, the total discharge Q2 being the summation of the infinitesimal discharges Q2 between the lower limit when gro, and the upper limit when discharge Q2 may be written,

since the total discharge (Q) of the weir is the sum of @fl-Q2, therefore,

But the total discharge Q must be directly proportional to the height of the surface of the liquid above the datum line MN, or, in other words, Q vmust be equal to (7H-Eta) multiplied by a constant quantity (K). Therefore, 4

yzt, the

and

To determine the value of K let t :0. 'Consequently the total discharge, Q, will be e .ual to the discharge, Q1, of the rectangle A LK, or,

Therefore,

K catlfzg (5) substituting this value for K in equation (4),

e/gatle te telt/ato tit-ta caajghwpgd,

zetter tt) am tyitt] )gwada Transposing,

tatyay gaat sha1 teh? (H+ tot] (6) VExpanding (7L-taht by the binomial theorem,

By .a well known theorem of mathematics *it is evident that tta/t@ is identical with,

and may be replaced by a series which, when integrated with respect to y and after substitution of the limits, Will give a resultant series identical with the` right hand member of equation (7) or in other words may be replaced by an ascending series in y in which the powers of y are such that the resultant series will be obtained as stated above.

spection that this condition is fulfilled when,

where A1, A2,. A3, etc., are constant coeficients Whose values are to be determined.

Substituting for its value as given in equation (8) .1 k u Allg Wt -fycly +A2l1/hy ypzdy-I-Aa) Lgt/hy s yzdy A41; yZw/hy y2dy+ etc. Integratingseparately each term of equation (9), he ,/t y dy ZAJJ gmAztz {g1-:ASW -I- #wa-A47# TM,gwn-Asks T--nAGt rrAJ ete. (10) Equating the right hand members of equations (7) and 10),

It is evident on in- I insegno The powers of 71.bein the same inboth y 7 2 7( members of this equation, he coecients are vien-As :riva-55 Wham@ is ZW-gg identical; hence W13-Venca 1=Z 2 i TAGE '7 Zigg u Aar-2 gna-T 1r-A2.: gaga/l l5 Az: I 2 1 @tamara Afvl flirt-tf.: Tief@ tfmfiz 2 e substituting the values of A A A etc. TgWiLg: il Af: "g-CU) A equation (8), 1 27 87 s m zz-i 21e.; 21er 21er agee, 2ten-e F37 y +vey uw @l +ve y gaa t tra @l *etc lezyeiyeiyeiyeiyeiye 'i g 5 *X-g-X-u'iil f l 11: ai ZXa-i-xa75 LXai-i-Q a ll 07T e Cdl D 2'- ,y l ,ial/Qs- @nl /Qu t.

But, I I y v Vigili il? lX/QLl/ :l l/lf +5 a) 7 q al +9 a 1l a +8136. Ahan. a Therefore l t minimum operative level be' in direct pro- 2Z 1 Q portion to the height orn liquid above the =ltim datum level.

2. A liquid meter rovided with a Weir or p 2 1 notch having an edge termed on a c0111-,y :1{1- 517ML {y} stantly changing curvature and extending a from the line of minimum operative level to which is the equation of the curve LU lwith reference to the aXes XX and YY. Y

In practice l make the height e small as compared with the total height of orifice to be utilized and helow the height of the liquid at which the meter is to be operated in practice. In any particular instance it may be made as small as desired and the proportional relation of head and discharge will still hold good for levels above level XX.` From the foregoing, it will he readily understood that owing to the fundamental property of the orifice each inch of increased head, for example, above the line XX,'in duoes a fixed increment in the amount of water discharged through the said orifice and that the several increments are mutually equal. Other shapes of orifice `giving similar results may also he used, but l have shown the preferred form.

l claim:

l. A liquid meter provided with a Weir notch having a datum level, 'a minimum operative level' above the datum level,'and

ka bottom. level below the datum level, the

width of the notch above the minimum operative level being such that the flow of liquid therethrough will at all levels above the the line of maximum operative level, said notch having its datum level below the linev of minimum operative level and its bottom edge below the datum level, the width ofthe notch between said maximum and minimum operative levels being such that the flow of liquid therethrough will at all levels above the minimum operative level be in direct proportion to the height of liquid above the datum level.

3. A liquid meter provided with a Weir notch having a datum level, a minimum operative level above the datum level, and a bottom level below the minimum operative level, the width of the notch above the minimum operative level being such that the flow of liquid therethrough will at all levels above the minimum operative level be in direct proportion to the height oi liquid above the datum level. Sept. eo/ie.

vieron eurno,

Administra/tor of the esitate 07' Harry Here bert Sutra, deceased.

ln presence o-.

VIOLA E. HUGHES, MAXWELL G. ELenRL-Y. 

